We prove that for every fixed k and 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2 . This answer...
Noga Alon, Rados Radoicic, Benny Sudakov, Jan Vond...
In the minimum path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that pa...
In this paper we present a protocol for sensor applications that require periodic collection of raw data reports from the entire network in a timely manner. We formulate the probl...
Given a graph G = (V, E) with n vertices, m edges and maximum vertex degree ∆, the load distribution of a coloring ϕ : V → {red, blue} is a pair dϕ = (rϕ, bϕ), where rϕ i...
Nitin Ahuja, Andreas Baltz, Benjamin Doerr, Ales P...
We study deterministic, distributed algorithms for two weak variants of the standard graph coloring problem. We consider defective colorings, i.e., colorings where nodes of a colo...